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A054393 Number of permutations with certain forbidden subsequences. 3
1, 1, 2, 5, 14, 42, 132, 428, 1417, 4757, 16119, 54963, 188219, 646460, 2224944, 7668915, 26461005, 91371594, 315689675, 1091166442, 3772747245, 13047503222, 45131078409, 156129312025, 540181837728, 1869097588540, 6467740095295 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

LINKS

Table of n, a(n) for n=0..26.

E. Barcucci et al., From Motzkin to Catalan Permutations, Discr. Math., 217 (2000), 33-49.

Nickolas Hein, Jia Huang, Variations of the Catalan numbers from some nonassociative binary operations, arXiv:1807.04623 [math.CO], 2018.

J. W. Layman, The Hankel Transform and Some of its Properties, J. Integer Sequences, 4 (2001), #01.1.5.

FORMULA

Conjecture: (-n+3)*a(n) + (10*n-33)*a(n-1) + 5*(-7*n+24)*a(n-2) + 2*(22*n-63)*a(n-3) + 2*(5*n-78)*a(n-4) + (-55*n+357)*a(n-5) + (22*n-135)*a(n-6) + 3*(-n+6)*a(n-7) = 0. - R. J. Mathar, Aug 09 2015

MATHEMATICA

a[0] = 1; a[n_] := Module[{M}, M = Table[If[j < i || i == j && i <= 5 || j == i+1, 1, 0], {i, 1, n}, {j, 1, n}]; MatrixPower[M, n][[1, 1]]];

Table[a[n], {n, 0, 26}] (* Jean-Fran├žois Alcover, Aug 16 2018, after A054391 *)

CROSSREFS

Interpolates between Motzkin numbers (A001006) and Catalan numbers (A000108).

Cf. A005773, A054391, A054392, A054394.

Sequence in context: A293499 A024175 A152226 * A261589 A036768 A287970

Adjacent sequences:  A054390 A054391 A054392 * A054394 A054395 A054396

KEYWORD

nonn,changed

AUTHOR

N. J. A. Sloane, Elisa Pergola (elisa(AT)dsi.unifi.it), May 21 2000

STATUS

approved

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Last modified October 20 04:37 EDT 2018. Contains 316378 sequences. (Running on oeis4.)